Fig. 6: DFT calculations and STEM simulations revealing the stabilization of the polar phase at the APBs in m-HfO2.

a–c Atomic structure models of the APB in HfO2 obtained by DFT structural relaxation, with the APB width of 2 u.c., 4 u.c., and 8 u.c., respectively. d–f HAADF images simulated by using the atomic structure models in (a–c). g-i ABF images simulated by using the atomic structure models in (a–c) and corresponding O-displacement vector maps at the APBs.